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About this video
ChatGPT sets three tough questions: a quadratic equation solved with the quadratic formula and again with the X method, two simultaneous equations solved by elimination, and an equation with x both in an exponent and outside it — found by inspection, then solved graphically, a challenge beyond CAPS.
What it covers
- The quadratic formula: substitute in brackets
- The same equation factorised with the X method
- Simultaneous equations by elimination, then substitute into the simpler equation
- Solving by inspection, and why every base cannot be made 2
- A graphical solution — beyond CAPS, a challenge
Extra worked examples
✍️ Extra example: solve 3x² − 7x + 2 = 0 with the quadratic formula, then check by factorising.
- 1a = 3, b = −7, c = 2Read them off with their signs.
- 2x = (−(−7) ± √((−7)² − 4(3)(2)))/(2(3))x = (−b ± √(b² − 4ac))/2a — substitute IN BRACKETS, so (−7)² is +49.
- 3= (7 ± √25)/6 = (7 ± 5)/649 − 24 = 25.
- 4x = 2 or x = 1/312/6 = 2 and 2/6 = 1/3.
- 5Check: (3x − 1)(x − 2) = 0 gives the same two answersFOIL: 3x² − 6x − x + 2 = 3x² − 7x + 2 ✓
✍️ Extra example: solve simultaneously by elimination: 2x + 3y = 12 and 5x − y = 13
- 115x − 3y = 39Multiply the second equation by 3, so the y-terms are opposites.
- 217x = 51 → x = 3Add the two equations: the y-terms cancel.
- 35(3) − y = 13 → y = 2Substitute into the simpler equation.
- 4Check: 2(3) + 3(2) = 12 ✓Check in the equation you did not substitute into.
Exercises to try
Work each one out, then click to reveal the answer.
- 1Solve 2x² + x − 6 = 0 with the quadratic formula.
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a = 2, b = 1, c = −6: x = (−1 ± √(1 + 48))/4 = (−1 ± 7)/4 → x = 3/2 or x = −2 - 2Factorise 2x² + x − 6, and check that it gives the same answers as question 1.
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(2x − 3)(x + 2) = 0 → x = 3/2 or x = −2 ✓ - 3Solve by elimination: x + 2y = 7 and 3x − 2y = 5.
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Add: 4x = 12 → x = 3; then 3 + 2y = 7 → y = 2 - 4Solve by elimination: 4x + 3y = 10 and 2x + y = 4.
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Multiply the second by 3: 6x + 3y = 12; subtract the first: 2x = 2 → x = 1, y = 2 - 5Find a whole-number solution of 3x = 9x by inspection.
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Try 1, 2, 3: 3³ = 27 = 9 × 3, so x = 3 (a graph shows a second solution near x = 0,13)
